Development and evaluation of galaxy shape measurement algorithms for radio interferometric data

The purpose of this Thesis is to develop, test, and characterize different models attempting to tackle the problem of measurement of galaxy shapes applied in interferometric observations. Shape measurement is a tool for estimating the underlying shear due to weak gravitational lensing by large-scale foreground matter distributions. The recent enormous progress in radio interferometric imaging during the last years, with projects such as MeerKAT, ASKAP, and in future SKA, motivates the development of advanced algorithms that utilize radio observations for this task. In most of these algorithms, the main disadvantage is that the proposed models' parameters have to be estimated in advance, assuming certain prior knowledge on the form of the objects. Our motivation is to develop and evaluate frameworks that do not require significant prior information on this form to make accurate measurements.To achieve this goal, we move in two implementation directions. In the first one, we are based on an existing approach that applies an object decomposition procedure using a dictionary of shapelet functions. Our proposal goes some steps forward trying to estimate this decomposition's key size parameter from a model built on advanced regularization. More specifically, we create an over-redundant dictionary formed as the concatenation of several groups of orthogonal shapelet basis functions with different parameters, and we use structured sparsity penalties to estimate the size parameter of the best group. As an alternative development strategy, we form an algorithm that employs multi-resolution least-squares analysis, which attempts to identify the size value that minimizes the relative residual in the fitting.The second path, instead of making the shape estimation directly on radio interferometric data, performs image reconstruction from the visibilities and measures the ellipticity of the objects in the resulting images. For this purpose, we adopt a sparsity averaging analysis algorithm that has been developed in the past and restores with high precision the intensity image from the visibilities. We also implement a similar framework that uses the CLEAN algorithm for image reconstruction, which helps compare the results between the two options and evaluate the quality of the measurements achieved.All our models are tested using a collection of simulated data that include objects of different profile types, ellipticity, size, orientation, and position in the field of view. The visibilities generation is done using either a simulated Gaussian profile coverage or a realistic SKA-like one. Additionally, we present an initial study of the same algorithms on real objects from the COSMOS survey.